Digital electronics are rapidly replacing their analog counterparts in many applications of signal processing such as consumer electronics, machine control, robotics, telephony, navigation to mention just a few. Also, computers using digital representations of signals are being used to process signals that may be acquired from an analog source or output to an analog device. Inherent in all these applications is the assumption that the underlying analog signal, such as sound, force, or light intensity, is being represented by a sequence of values corresponding to the amplitude of the signal sampled at fixed intervals. The discreet values are stored in digital format as a sequence of integers. In some applications, such as digital music on a compact disk, an entire signal is stored, but only fetched or examined value by value. In other applications, such as telephony and robotics control, the digital signal is transient and is being processed in real time.
In most applications of digital signal processing there are two conversion phases: 1) the original analog input signal is converted to a digital sequence by an A/D converter, and eventually, 2) a possibly altered digital sequence is converted to the output analog signal by a D/A converter. The input process is called sampling and is done at a frequency chosen for the application. The reconstructed analog output signal is generated by holding a constant voltage for each interval using the values in the digital sequence in turn. This sample-hold paradigm is inherent in D/A converters used in most digital electronic applications.
A basic limitation or drawback of the known methods of reconstruction of an analog signal from its digital representation is that the conversion process forces the output analog function to be a non-continuous piecewise constant function, but does not force the choice of the representing function.
An important technological area in which this type of digital processing limitation is problematic is in robotic force control. Specifically, when a robotic device is used to present a human operator with forces that simulate, for example, contact with a wall then it is commonly observed that the virtual wall feels "alive". Rather than the wall acting as a passive barrier, the virtual wall appears to exert a repulsive force so that the return signal coming back from the robot appears to have acquired energy not present in the collision with the wall. This failure to accurately simulate contact also occurs when the robot that presents the human operator with force is connected, via a digital link, with a remote robot that is commanded to interact with real objects and reports the force of interaction over the digital link. In both cases energy appears to have been acquired. The inventors have determined that the error in the energy is proportional to the square of the error in the force. Since the energy is determined by the force-time integral (area under the curve of the force signal) this suggests that finding a piecewise constant function that reduces the area difference with the original continuous signal would have superior behaviour in controlling the robot.
It would therefore be advantageous to provide a method of signal processing that gives an analog output signal reconstructed from a digital representation of the original analog input signal such that its integral more closely tracks the integral of the original input signal.